Two-Weight Norm, Poincaré, Sobolev and Stein–Weiss Inequalities on Morrey Spaces

Abstract

We establish two-weight norm inequalities for singular integral operators and fractional integral operators on Morrey spaces. As a consequence of these inequalities, we obtain two-weight Poincaré and Sobolev inequalities on Morrey spaces. Moreover, we also establish the Stein–Weiss inequality, the Hardy inequality and the Rellich inequality on Morrey spaces.